What is the ((-9x^2+12x+24)/((x^2-5x-6)^2))^' ?

The ((-9x^2+12x+24)/((x^2-5x-6)^2))^' is (6(3x^3-6x^2+12x+28))/((x^2-5x-6)^3)

What is the first ((-9x^2+12x+24)/((x^2-5x-6)^2))^' ?

The first ((-9x^2+12x+24)/((x^2-5x-6)^2))^' is (6(3x^3-6x^2+12x+28))/((x^2-5x-6)^3)

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(\frac{- 9 x ^{2} + 12 x + 24}{( x ^{2} - 5 x - 6 ) ^{2}})^{^{'}}

\frac{6 ( 3 x ^{3} - 6 x ^{2} + 12 x + 28 )}{( x ^{2} - 5 x - 6 ) ^{3}}

Solution steps

(\frac{- 9 x ^{2} + 12 x + 24}{( x ^{2} - 5 x - 6 ) ^{2}})^{'}

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{( - 9 x ^{2} + 12 x + 24 ) ^{^{'}} ( x ^{2} - 5 x - 6 ) ^{2} - ( ( x ^{2} - 5 x - 6 ) ^{2} ) ^{^{'}} ( - 9 x ^{2} + 12 x + 24 )}{( ( x ^{2} - 5 x - 6 ) ^{2} ) ^{2}}

(- 9 x^{2} + 12 x + 24)^{'} = - 18 x + 12

((x^{2} - 5 x - 6)^{2})^{'} = 2 (x^{2} - 5 x - 6) (2 x - 5)

= \frac{( - 18 x + 12 ) ( x ^{2} - 5 x - 6 ) ^{2} - 2 ( x ^{2} - 5 x - 6 ) ( 2 x - 5 ) ( - 9 x ^{2} + 12 x + 24 )}{( ( x ^{2} - 5 x - 6 ) ^{2} ) ^{2}}

Simplify

\frac{( - 18 x + 12 ) ( x ^{2} - 5 x - 6 ) ^{2} - 2 ( x ^{2} - 5 x - 6 ) ( 2 x - 5 ) ( - 9 x ^{2} + 12 x + 24 )}{( ( x ^{2} - 5 x - 6 ) ^{2} ) ^{2}} : \frac{6 ( 3 x ^{3} - 6 x ^{2} + 12 x + 28 )}{( x ^{2} - 5 x - 6 ) ^{3}}

= \frac{6 ( 3 x ^{3} - 6 x ^{2} + 12 x + 28 )}{( x ^{2} - 5 x - 6 ) ^{3}}

\int \frac{( x ^{3} + 36 )}{x ^{2} + 36} d x

\int 4 cos (2 θ) d θ

\frac{d}{d x} (2^{(3 x)})

\int r^{2} cos (θ) d r

\frac{d}{d x} (9 + 6 x)

What is the ((-9x^2+12x+24)/((x^2-5x-6)^2))^' ?
The ((-9x^2+12x+24)/((x^2-5x-6)^2))^' is (6(3x^3-6x^2+12x+28))/((x^2-5x-6)^3)
What is the first ((-9x^2+12x+24)/((x^2-5x-6)^2))^' ?
The first ((-9x^2+12x+24)/((x^2-5x-6)^2))^' is (6(3x^3-6x^2+12x+28))/((x^2-5x-6)^3)